In a large saucepan coated with cooking spray, cook the onions, carrots and celery in butter for 3 minutes. Add the broccoli; cook 3 minutes longer. Stir in 2-3/4 cups milk, salt, thyme and pepper.
Bring to a boil, Reduce heat; cover and simmer 5-10 minutes or until veggies are tender. Combine the flour and remaining milk until smooth; gradually stir into the soup. Bring to a boil; cook 2 minutes longer or until thickened.